# Permanent Index (PI)

### Permanent Index (PI): Overview

***

 PI consists of an equally weighted tri-part asset composition:

* **⅓ $AO Token**
* **⅓ $AR Token**
* **⅓ Fair Launched Ecosystem Assets (FLPs)**

***

***

#### Foundation

The Permanent Index maintains its composition according to the following equation:

$$
PI = \frac{1}{3}AO + \frac{1}{3}AR + \frac{1}{3}\sum\_{i=1}^{n}FLP\_i
$$

Where:

$$
\begin{aligned}
AO,\ AR &= \text{fixed proportions of the total index} \\
FLP\_i &= \text{individual Fair Launched Project assets dynamically} \\
&\quad\text{selected based on market criteria}
\end{aligned}
$$

***

### Mint 

***

#### Overview of Key Parameters

| Notation                                         | Description                                    | Example |
| ------------------------------------------------ | ---------------------------------------------- | ------- |
| $$AO$$                                           | The $AO Token                                  | -       |
| $$AR,\ FLP\_i$$                                  | Underlying assets held by $$PI$$               | -       |
| <p><span class="math">PI</span></p><p></p>       | Current circulating supply of $Pi tokens       | 10,000  |
| <p><span class="math">V\_{\Pi}</span></p><p></p> | Total value (in $AO) of all assets held by PI  | 20,000  |
| $$AO\_{u}$$                                      | Amount of $AO delegated by a user              | 600     |
| $$AO\_{p}$$                                      | <p>Amount of $AO<br>delegated by a project</p> | 1,200   |

***

### Token Minting Mechanism (Proportional Issuance)

When $AO$ tokens are delegated to $\Pi$, they're immediately divided into three equal portions:

* One-third remains as $AO
* One-third is used to acquire $AR
* One-third is invested into selected Fair Launched Project assets ($FLP\_i$).

The amount of $\Pi$ tokens minted is proportional to the user's contribution relative to the total value of assets within the index.

**Formula (for Users):**

$$
\Pi\_{u} = \frac{AO\_{u} \times \Pi}{V\_{\Pi}}
$$

**Example:**

$$
\begin{aligned}
\text{For }AO\_{u}&=600,\quad \Pi=10{,}000,\quad V\_{\Pi}=20{,}000:\\
\Pi\_{u}&=\frac{600\times10{,}000}{20{,}000}=300
\end{aligned}
$$

*Interpretation:* A user delegating **600 AO tokens** receives **300 new $\Pi$ tokens**, reflecting their proportional share of the index's total assets.

***

### Token Minting for Fair-Launched Projects

Projects launching via Fair Launch similarly delegate $AO$ tokens, split equally into the three asset categories. Their issued tokens also maintain proportional fairness.

**Formula (for Projects):**

$$
\Pi\_{p} = \frac{AO\_{p} \times \Pi}{V\_{\Pi}}
$$

**Example:**

$$
{For } AO\_{p}=1,200,\ \Pi=10,000,\ V\_{\Pi}=20,000:\quad
\Pi\_{p}=\frac{1,200 \times 10,000}{20,000}=600
$$

$$
\Pi\_{p}=\frac{1,200 \times 10,000}{20,000}=600
$$

*Interpretation:* A project receives **600 $\Pi$ tokens** upon delegating **1,200 AO tokens**.

***


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://docs.autonomous.finance/core-financial-infrastructure/permanent-index-pi.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.